A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence

A005244 on the OEIS · family self-referential

Weight–level plate of A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence — Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.

Open in the 3-D viewer A005244 on the OEIS

Terms	100,000 (n = 1 … 100,000)
Decomposable (a > 2d)	99,995
Level class, k > L	22,242 · 22.24 %
Weight class, k ≤ L	77,753 · 77.76 %
Ties, k = L	143
On the level line L = 1	16,135
Forced level, l ≤ d²	9
Range of a(n)	2 … 236,249
Range of the jump d	1 … 21
Largest weight k, level L	236,209, 118,118

21 different gaps occur, from 1 to 21; the level share is 22.24 %; L = 1 holds 73 % of the level class.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.